The present invention relates generally to photonic crystals that exhibit a substantially vanishing refractive index and a finite impedance, and more particularly to photonic crystals that exhibit such properties for one or more frequencies in the optical regime.
The field of metamaterials has received a great deal of attention and has progressed rapidly over the last decade The earliest and most cited property of metamaterials, i.e., negative refractive index, has already been demonstrated in potential applications in superlens imaging and rainbow-trapping. Another exotic property, zero refractive index, can be employed in supercoupling and cloaking applications. For example, using an anisotropic positive refractive index from zero to one, a cloak can be built based on transformation optics.
At present, the negative/zero/positive refractive index is usually achieved by following well-established physical principles: 1) plasmonics; 2) metallic resonators; 3) periodically L-C loaded transmission lines; and 4) dielectric resonators.
For example, in some conventional metamaterials, to realize a zero refractive index for a specific wavelength λ, a periodic array of scatters is employed, each of which generates an electric or magnetic flux loop. The scatters are configured such that the flux loops are canceled by those of neighboring scatters due to multiple interferences, thus achieving εeff=0 or μeff=0 effectively, resulting in a zero effective index (neff=(εeff·μeff)1/2=0). However, such structures exhibit infinite or zero impedance (μeff/εeff)1/2 for the propagation of electromagnetic waves. As such, In electromagnetic waves cannot be coupled into such conventional zero-index metamaterials (ZIM) from free space or waveguide structures without implementing a specific impedance matching technique.
Thus, the conventional metamaterials can have certain shortcomings. For example, the negative (zero) refractive index provided by plasmonics, metallic, and Mie-resonance-based non-metallic metamaterials is usually associated with high losses and mismatched impedance. These drawbacks decrease the performance of those metamaterials dramatically so as to limit their potential applications.
Accordingly, there is a need for enhanced metamaterials exhibiting, e.g., zero or negative, indices of refraction, and concurrently exhibiting a finite impedance.